U.S. patent number 5,499,319 [Application Number 08/181,373] was granted by the patent office on 1996-03-12 for fuzzy logic controller.
Invention is credited to Talib H. Al Janabi, Labib Sultan.
United States Patent |
5,499,319 |
Al Janabi , et al. |
March 12, 1996 |
Fuzzy logic controller
Abstract
This invention relates to a design and implementation of
real-time knowledge-based fuzzy controller system for general
purpose industrial applications. The invention relates to the
design of an Intelligent system which implements a decision-making
procedure based on approximation, association and reasoning with
fuzzy patterns and their clearness assessments rather than the use
of Max-Min computation over fuzzy relational matrices usually
applied in approximate reasoning procedures in similar systems.
According to this design fuzzy controller is a device which
operates at the level of fuzzy pattern processing where each
control task is expressed through the attributes of fuzzy patterns
(syntax and content, domain and clearness measure), and the
elementary cognitive activities which the human performs with these
patterns such as: recognition, generation, assessment, association,
pattern matching, approximation, etc. The fuzzy controller utilizes
a new scheme for approximate reasoning with fuzzy patterns called
the Clearness Transformation Rule of Inference (CTRI). This
mechanism offers a spectrum of advantages broadening the functional
Intelligence of the controller to handle complex human rusks,
improving performance and accuracy of the controller and reduces
the computational requirements. The fuzzy controller presented in
the invention can be applied in general engineering practice,
financial, medical, process control, pattern recognition and other
areas requiring knowledge-based behaviour in decision making.
Inventors: |
Al Janabi; Talib H. (Ottawa,
Ontario, CA), Sultan; Labib (Willowdale, Ontario,
CA) |
Family
ID: |
25080746 |
Appl.
No.: |
08/181,373 |
Filed: |
January 14, 1994 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
Issue Date |
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767839 |
Sep 30, 1991 |
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Current U.S.
Class: |
706/1;
706/52 |
Current CPC
Class: |
G06N
7/04 (20130101); G05B 13/0275 (20130101) |
Current International
Class: |
G06N
7/00 (20060101); G05B 13/02 (20060101); G06N
7/04 (20060101); G06F 009/44 () |
Field of
Search: |
;395/3,61,900,51,22 |
References Cited
[Referenced By]
U.S. Patent Documents
Other References
Procyk et al., "A Linguistic Self-Organizing Process Controller",
Automatica, vol. 15, 1979, 15-30. .
Togai et al., "Expert System on a Chip: An Engine for Real-Time
Approximate Reasoning", IEEE Expert, Fall 1986, 55-62. .
Leung et al., "Fuzzy Concepts in Expert Systems" IEEE Computer,
Sep. 1988, 43-56. .
Sugiyama, K., "Rule-Based Self-Organising Controller", Fuzzy
Computing, 1988, 341-353. .
Lim et al., "Implementing Fuzzy Rule-Based Systems on Silicon
Chips", IEEE Expert, Feb. 1990, 31-45. .
Watanabe et al., "A VLSI Fuzzy Logic Controller with
Reconfigurable, Cascadable Architecture", Intl. Jou. Solid-State
Circuits, Apr. 1990, 376-382. .
Zhijian et al., "A CMOS Current-Mode High Speed Fuzzy Logic
Microprocessor for a Real-Time Expert System", Proc. 20th Intl.
Symp. on Multi-Valued Logic, May 1990, 394-400. .
Bowen, et al., "Conflict Resolution in Fuzzy Forward Chaining
Production Systems", AAAI88, Aug. 1988, 117-121. .
Sultan, L., "A Formal Approach for the Organization and
Implementation of Fuzzy Micro-Processor Module," Fuzzy Computing,
1988, 201-221..
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Primary Examiner: Downs; Robert W.
Parent Case Text
This application is a continuation, of application Ser. No.
07/767,839, filed Sep. 30, 1991, now abandoned.
Claims
The embodiments of the invention in which an exclusive property or
privilege is claimed are defined as follows:
1. A fuzzy logic decision-maker for receiving input signals,
utilizing data in a knowledge-base and, based on said input signals
and said data, providing output signals in order to provide
knowledge-based decision making, said knowledge-base of the type
containing
fuzzy rules comprising representations of fuzzy patterns of
consequents (THENs) and representations of fuzzy patterns of
antecedents (IFs);
clearness distributions comprising collections of representations
of clearness degrees, said clearness degrees defining cognitive
measures which assess the fuzziness of fuzzy patterns, and
representations of thresholds of transitions, said thresholds of
transitions being the intersection points of every two adjacent
clearness distributions,
said fuzzy logic decision-maker comprising:
a fuzzifier comprising first means for mapping said input signals
into representations of input fuzzy patterns and second means for
mapping said input signals into representations of input clearness
degrees of said input fuzzy patterns, said input clearness degrees
being valued in the interval of zero to one, where zero represents
"absolutely unclear" ("absolutely false") and one represents
"absolutely clear" ("absolutely true");
pattern matching and rule selection means for receiving said
representations of input fuzzy patterns from said first means of
said fuzzifier and, responsive thereto, for selecting one rule from
said knowledge-base, and for generating representations of output
fuzzy patterns based on the consequent (THEN) portion of said
rule;
approximate reasoning means for receiving said representations of
input clearness degrees from said second means of said fuzzifier
and for mapping said representations of input clearness degrees
into a representation of an output clearness degree, said
approximate reasoning means operating in parallel with said pattern
matching and rule selection means; and
defuzzifier means for receiving said representations of output
fuzzy patterns from said pattern matching and rule selection means
and for receiving said representation of an output clearness degree
from said approximate reasoning means and for mapping said
representations of output fuzzy patterns and said representation of
an output clearness degree into said output signals.
2. The fuzzy logic decision-maker of claim 1 in which said
fuzzifier first means comprises means to compare said input signals
with said representations of thresholds of transitions contained in
said knowledge-base such that each of said input signals is mapped
into a corresponding representation of a fuzzy pattern.
3. The fuzzy logic decision-maker of claim 2 in which said
fuzzifier second means receives said input signals and said
representations of input fuzzy patterns generated by said fuzzifier
first means from said input signals, said fuzzifier second means
comprising means for selecting a clearness distribution from said
knowledge-base corresponding to each of said input fuzzy patterns,
and means for utilizing each said clearness distribution, and the
input signal utilized by said fuzzifier first means in generating
the representation of the fuzzy pattern which corresponds to said
clearness distribution, to generate a representation of a clearness
degree.
4. The fuzzy logic decision-maker of claim 3 wherein said clearness
distribution is mapped into a pre-determined number of discrete
clearness degrees.
5. The fuzzy logic decision-maker of claim 3 wherein each clearness
distribution has an x-axis representing the range of input variable
values for the fuzzy pattern which is associated with the input
variable and which corresponds with said each clearness
distribution and a y-axis representing clearness degrees and
wherein said means for utilizing each said clearness distribution,
and the input signal utilized by said fuzzifier first means in
generating the representation of the fuzzy pattern which
corresponds to said clearness distribution, locates said input
signal on the x-axis of said clearness distribution and projects
said input signal onto the y-axis of said clearness distribution in
order to obtain the clearness degree of said input fuzzy pattern
for said input signal.
6. The fuzzy logic decision-maker of claim 3 wherein said
defuzzifier means comprises means for selecting a clearness
distribution from said knowledge-base corresponding to each of said
output fuzzy patterns, and means for utilizing each said output
fuzzy pattern clearness distribution to map said representation of
an output clearness degree to a value for one of said control
signals.
7. The fuzzy logic decision-maker of claim 6 wherein said output
fuzzy pattern clearness distribution is mapped into a
pre-determined number of clearness degrees.
8. The fuzzy logic decision-maker of claim 6 wherein each clearness
distribution has an x-axis representing the range of output
variable values for the fuzzy pattern which is associated with the
output variable and which corresponds with said each clearness
distribution and a y-axis representing clearness degrees and
wherein said means for utilizing each said output fuzzy pattern
clearness distribution to map said representation of an output
clearness degree to a value for one of said control signals
comprises means for locating said output clearness degree on the
y-axis of said output fuzzy pattern clearness distribution and for
projecting said output clearness degree onto the x-axis of said
output fuzzy pattern clearness distribution.
9. The fuzzy logic decision-maker of claim 1 wherein said
representations of input fuzzy patterns comprise indices, names, or
addresses of said input fuzzy patterns and wherein said
representations of output fuzzy patterns comprise indices, names,
or addresses of said output fuzzy patterns.
10. The fuzzy logic decision-maker of claim 1 wherein said means
for mapping of said approximate reasoning means comprises means for
determining the minimum value of input clearness degrees
represented by said representations of input clearness degrees and
for assigning said minimum value to the output clearness degree
represented by said representation of an output clearness
degree.
11. The fuzzy logic decision-maker of claim 1 wherein said means
for mapping of said approximate reasoning means comprises means for
determining the maximum value of input clearness degrees
represented by said representations of input clearness degrees and
for assigning said maximum value to the output clearness degree
represented by said representation of an output clearness
degree.
12. The fuzzy logic decision-maker of claim 1 wherein said means
for mapping of said approximate reasoning means comprises means for
determining the average value of input clearness degrees
represented by said representations of input clearness degrees and
for assigning said average value to the output clearness degree
represented by said representation of an output clearness
degree.
13. A fuzzy logic controller for receiving input signals from a
process, utilizing data in a knowledge-base and, based on said
process input signals and said data, providing output control
signals to said process in order to provide knowledge-based control
of said process, said knowledge-base of the type containing
fuzzy rules comprising representations of fuzzy patterns of
consequents (THENs) and representations of fuzzy patterns of
antecedents (IFs);
clearness distributions comprising collections of representations
of clearness degrees, said clearness degrees defining cognitive
measures which assess the fuzziness of fuzzy patterns, and
representations of thresholds of transitions, said thresholds of
transitions being the intersection points of every two adjacent
clearness distributions,
said fuzzy logic controller comprising:
a fuzzifier comprising first means for mapping said process input
signals into representations of input fuzzy patterns and second
means for mapping said process input signals into representations
of input clearness degrees of said input fuzzy patterns, said input
clearness degrees being valued in the interval of zero to one,
where zero represents "absolutely unclear" ("absolutely false") and
one represents "absolutely clear" ("absolutely true");
pattern matching and rule selection means for receiving said
representations of input fuzzy patterns from said first means of
said fuzzifier and, responsive thereto, for selecting one rule from
said knowledge-base, and for generating representations of control
action fuzzy patterns based on the consequent (THEN) portion of
said rule;
approximate reasoning means for receiving said representations of
input clearness degrees from said second means of said fuzzifier
and for mapping said representations of input clearness degrees
into a representation of a control action clearness degree, said
approximate reasoning means operating in parallel with said pattern
matching and rule selection means; and
defuzzifier means for receiving said representations of control
action fuzzy patterns from said pattern matching and rule selection
means and for receiving said representation of a control action
clearness degree from said approximate reasoning means and for
mapping said representations of control action fuzzy patterns and
said representation of a control action clearness degree into said
output signals.
14. The fuzzy logic controller of claim 13 in which said fuzzifier
first means comprises means to compare said process input signals
with said representations of thresholds of transitions contained in
said knowledge-base such that each of said process input signals is
mapped into a corresponding representation of a fuzzy pattern.
15. The fuzzy logic controller of claim 14 in which said fuzzifier
second means receives said process input signals and said
representations of input fuzzy patterns generated by said fuzzifier
first means from said process input signals, said fuzzifier second
means comprising means for selecting a clearness distribution from
said knowledge-base corresponding to each of said input fuzzy
patterns, and means for utilizing each said clearness distribution,
and the input signal utilized by said fuzzifier first means in
generating the representation of the fuzzy pattern which
corresponds to said clearness distribution, to generate a
representation of a clearness degree.
16. The fuzzy logic controller of claim 15 wherein each clearness
distribution has an x-axis representing the range of input variable
values for the fuzzy pattern which is associated with the input
variable and which corresponds with said each clearness
distribution and a y-axis representing clearness degrees and
wherein said means for utilizing each said clearness distribution,
and the process input signal utilized by said fuzzifier first means
in generating the representation of the fuzzy pattern which
corresponds to said clearness distribution, locates said process
input signal on the x-axis of said clearness distribution and
projects said process input signal onto the y-axis of said
clearness distribution in order to obtain the clearness degree of
said input fuzzy pattern for said input signal.
17. The fuzzy logic controller of claim 15 wherein said means for
mapping of said approximate reasoning means comprises means for
determining the minimum value of input clearness degrees
represented by said representations of input clearness degrees and
for assigning said minimum value to the control action clearness
degree represented by said representation of a control action
clearness degree.
18. The fuzzy logic controller of claim 15 wherein said means for
mapping of said approximate reasoning means comprises means for
determining the maximum value of input clearness degrees
represented by said representations of input clearness degrees and
for assigning said maximum value to the control action clearness
degree represented by said representation of a control action
clearness degree.
19. The fuzzy logic controller of claim 15 wherein said means for
mapping of said approximate reasoning means comprises means for
determining the average value of input clearness degrees
represented by said representations of input clearness degrees and
for assigning said average value to the control action clearness
degree represented by said representation of a control action
clearness degree.
20. The fuzzy logic controller of claim 15 wherein said defuzzifier
means comprises means for selecting a clearness distribution from
said knowledge-base corresponding to each of said control action
fuzzy patterns, and means for utilizing each said control action
fuzzy pattern clearness distribution to map said representation of
a control action clearness degree to a value for one of said
process control signals.
21. The fuzzy logic controller of claim 20 wherein each clearness
distribution has an x-axis representing the range of control action
values for the fuzzy pattern which is associated with the control
action and which corresponds with said each clearness distribution
and a y-axis representing clearness degrees and wherein said means
for utilizing each said control action fuzzy pattern clearness
distribution to map said representation of a control action
clearness degree to a value for one of said control signals
comprises means for locating said control action clearness degree
on the y-axis of said control action fuzzy pattern clearness
distribution and for projecting said control action clearness
degree onto the x-axis of said control action fuzzy pattern
clearness distribution.
22. A method for controlling a process having process signals
comprising the following steps:
mapping said process signals into representations of input fuzzy
patterns;
mapping said process signals into representations of input
clearness degrees of said input fuzzy patterns, said input
clearness degrees defining cognitive measures which assess the
fuzziness of input fuzzy patterns, said input clearness degrees
being valued in the interval of zero to one, where zero represents
"absolutely unclear" ("absolutely false") and one represents
absolutely clear" ("absolutely true");
selecting a fuzzy rule from a collection of fuzzy rules of the type
comprising representations of fuzzy patterns of consequents (THENs)
and representations of fuzzy patterns of antecedents (IFs) having
an antecedent matching said representations of input fuzzy
patterns;
generating representations of control action fuzzy patterns based
on the consequent (THEN) portion of said selected rule;
while selecting a fuzzy rule, mapping said representations of input
clearness degrees into a representation of a control action
clearness degree, each said control action clearness degree
defining cognitive measures which assess the fuzziness of control
action fuzzy patterns; and
mapping said representations of control action fuzzy patterns and
said representation of a control action clearness degree into
output signals and inputting said process with said output signals
in order to control said process.
23. The method of claim 22 wherein said step of mapping said
process signals into representations of input fuzzy patterns
comprises comparing each of said process signals with
representations of thresholds of transitions, said thresholds of
transitions being the intersection points of every two adjacent
clearness distributions, said clearness distributions comprising
collections of representations of clearness degrees, and selecting
an input fuzzy pattern based on each such comparison.
Description
BACKGROUND
Existing fuzzy controller designs are based on the Compositional
Rule of Inference (CRI) for approximate reasoning of L. A. Zadeh.
This approach applies the notion of membership function to measure
the compatibility of fuzzy linguistic categories, such as HIGH, LOW
etc., with the crisp and deterministic values (usually measured,
calculated or assigned) which are utilized to describe the state of
the process variables and objects, such as TEMPERATURE, PRESSURE,
etc. In this approach, the control rules (acquired from experts)
are interpreted in the controller knowledge-base as fuzzy relations
which are represented as fuzzy matrices. For multivariable
processes these matrices become multi-dimensional. The inference
and approximate reasoning procedure of the CRI is performed using
the time-consuming Max-Min operations over these matrices. As a
result the operation of the controller can handle slow and simple
processes but may face difficulties to cope with real-time
applications for fast and complex multivariable processes due to
the huge computations required to implement their functionality.
Another principal limitation on the CRI based fuzzy controllers is
that they perform reasoning at the fuzzy data level (where the
rules and membership functions are mapped into matrices) and can
not perform reasoning at the level of fuzzy patterns as the human
usually does in handling the real world situations. This makes it
difficult to use these controllers to simulate the various
functionalities of human thinking which usually manipulates
patterns in the problem solving practice, not massive data
processing. Another difficulty faced by the CRI based fuzzy
controllers is that they are unable to generate scenarios and
records to describe their behaviour in terms of the tasks and
patterns they simulate in their operations so that they may be used
to match the human behaviour involved in similar control tasks.
This is due to the algorithmic rather than cognitive bases of the
approximate reasoning procedure of the CRI employed in these
controllers. The compatibility between the operation of fuzzy
controller devices and the human thinking is an important issue
required for enhancing the functional intelligence of these
controllers and for simplifying the acquisition of the knowledge
from experts which, in turn, shortens the time of application
development.
Other relevant literature includes:
1) Rasmussen, Information processing and Human-Machine Interaction.
An Approach to Cognitive Engineering. Noah-Holland, 1986.
2) Sultan, "A composition of binary and multivalued logic for the
procedures organization of fuzzy expert systems," IEEE Proceedings
on ISMVL, pp. 154-159, 1984.
3) Sultan, "Some considerations on systems organization for fuzzy
information processing", in: Trapple L. (ed.), Cybernetics and
system research, North-Holland, pp. 551-556, 1984.
4) L. Sultan, "A formal approach for the organization and
implementation of fuzzy micro- processor module", Fuzzy Computing,
pp. 201-221, 1988.
5) Zadeh, "Outline of a new approach to the analysis of complex
systems and decision processes," IEEE Trans Systems, Man and
Cybernetics., vol. SMC-3, pp. 28-44, 1973.
6) L. A. Zadeh, "The concept of a linguistic variable and its
application to approximate reasoning, I and II", Inform. Sci., vol.
8, pp. 199-249 and vol. 9, pp. 301-357, 1975.
SUMMARY OF THE INVENTION
This invention is based on the premise that, in order to make their
decisions, humans do not perform massive number manipulation and
matrix multiplication which are computation intensive, such as how
the CRI operates. Instead they perform comparisons, associations,
approximations and assessments. Humans operate on, and manipulate,
fuzzy patterns in making their decisions. Fuzzy patterns are the
pictures which we draw in our minds about the real world events
where these pictures have varying degrees of clearness and
vagueness which enable us perceive these events with varying
degrees of clarity (fuzziness). Evidently a more efficient, and a
more intelligent, fuzzy controller design is that which operates on
these same principles.
The fuzzy controller presented in this invention is designed on the
basis of these premises. It is an intelligent device which operates
and makes decisions by processing fuzzy patterns and by performing
association and approximation and not through employing intensive
matrix computations of fuzzy data. It is capable of performing the
tasks of recognition, generation and assessment of validity
measures of fuzzy patterns of the real world situations. The
controller reasons with these patterns and their clearness degrees
to arrive at its decisions. In this design the necessity to use
fuzzy matrices and the time consuming Max-Min operations for
approximate reasoning are eliminated. The controller becomes
fast-acting real-time operating device for decision-making even in
complex and multivariable applications. Its behaviour and decisions
can be traced back and validated explicitly which simplifies the
acquisition and optimization of the control and expert knowledge.
This invention provides a systematic approach for the design of
fuzzy controllers and decision making systems. In this design the
controller algorithm is not amalgamated with the knowledge-base as
it is the case with the CRI based fuzzy controllers. Instead the
algorithm and the knowledge-base are kept separate from each other
making the controller a true artificial intelligence system.
To accomplish the foregoing and other objects, and in accordance
with the present invention, as described and embodied herein, a
system called the Clearness Transformation Fuzzy Logic Controller
(CTFLC) is presented embodying the organization, as well as, the
scheme of implementation of a fuzzy controller and decision-maker
system. In this system the measured process values are received as
crisp data input and according to which control actions are
generated in the form of crisp data as output control commands, or
the input is in the form of fuzzy patterns and linguistic scenarios
and the output is in the form of control commands or control action
patterns and scenarios which may be utilized by the operator to
enhance his/her decisions about the process operation. The fuzzy
controller establishes its output through the execution of a series
of knowledge based tasks such as situation recognition, situation
assessment in terms of clearness degrees, pattern matching and the
deduction of the control action pattern, approximate reasoning to
determine the clearness assessments of the control action patterns,
and defuzzification of the control pattern (if the output of the
controller is required in the form of crisp data values).
The following are the distinguished functional and operational
characteristics and advantages of the CTFLC system.
1. It is a system for general purpose applications capable of
simulating human thinking in handling the tasks of fuzzy control
and decision-making. These tasks are based on a cognitive model of
fuzzy control defined in the description of the invention.
2. It is a device which operates by processing fuzzy patterns (as
basic entities or portions of information) to achieve the tasks of
control and decision making. It implements a set of knowledge-based
tasks such as generation, recognition and assessment of the
validity of fuzzy patterns and achieves approximation in the
association between these patterns producing control and decision
patterns together with their validity assessments. With these
capabilities the CTFLC can be employed as a fuzzy controller,
intelligent decision-maker and a decision support system.
3. It applies a new scheme for approximate reasoning which
eliminates the necessity to use the time consuming Max-Min
computation usually employed for approximate reasoning in other
similar devices. Hence, the CTFLC can operate in real-time when
applied for control and decision-making in multivariable systems
and complex processes.
4. Its organization and operating principles are independent of the
technology employed for its implementation. Various technological
bases can be used to implement it while the same operation and
design principles are maintained. This characteristic of the CTFLC
gives it the capability of integration with other systems.
5. The controller architecture and design are such that the
knowledge-base is kept separate from the algorithm. This simplifies
the process of knowledge acquisition and optimization, and assists
in the rapid development of applications and in the validation of
the controller performance.
Other objects and advantages of the invention will be apparent from
the forthcoming description and claims of the invention including
the a detailed description of the drawings in which:
BRIEF DESCRIPTION OF DRAWINGS
FIG. (1) is a scheme illustrating the organization of the cognitive
model of fuzzy control upon which the invention of the CTFLC system
is based.
FIG. (2) is a scheme illustrating the modules and operational
phases of the CTFLC system used for the embodiment of the
invention.
FIG. (3) is a scheme illustrating the internal architecture of the
CTFLC system at the level of the operational modules and the
knowledge used by each each module used for the embodiment of the
invention.
FIG. (4) is an analysis in the form of tables of the
characteristics of tasks of the CTFLC system in terms of
input-output data, knowledge and control strategies required for
their accomplishment used for the embodiment of the CTFLC system of
the invention.
FIG. (5) is a functional diagram of the Fuzzifier at the level of
input-output data which illustrates the interaction between the two
module: Fuzzifier-I and Fuzzifier-II used for the implementation of
the preferred embodiment of the invention.
FIG. (6) is a diagram showing the preferred off-line generation of
the values of the thresholds of transition (TT) using the clearness
distributions of fuzzy patterns used for the implementation of the
Fuzzifier of the invention.
FIG. (7) is a diagram illustrating the preferred off-line
generation of the values of the clearness level thresholds (CL)
used for the implementation of the Fuzzifier of the invention.
FIG. (8) is a functional diagram of the Defuzzifier module at the
level of input-output data used for the implementation of the
invention.
FIG. (9) is a diagram illustrating the principle of
counter-reflection of the clearness level of a fuzzy pattern on the
elements of the domain space to infer crisp data of the control
action to the process, used for the implementation of the
Defuzzifier of the invention.
FIG. (10) is a table showing the preferred embodiment of the CTFLC
database system for the software implementation of the
invention.
DETAILED DESCRIPTION OF THE INVENTION
THE COGNITIVE MODEL OF FUZZY CONTROL
The functionality, design and operational principles of the
Clearness Transformation Fuzzy Logic Controller (CTFLC) are based
on the cognitive model of fuzzy control and decision-making. The
general diagram of this model is presented in FIG. (1). It
illustrates the basic tasks and cognitive mechanisms of a human
involved in the control and decision-making procedure at a
rule-based, and knowledge-based, level of behaviour. This model has
been established through psychological, cognitive and experimental
studies using the model of Rasmussen for supervisory control and
decision-making as a frame-work. Applying this model, the tasks
which the human performs when making decisions were analyzed and
characterized as a loop of three phases. These are: (a)
observation, detection and assessment of situation patterns, (b)
control action planning and (c) action execution. The model of FIG.
(1) reflects these phases. Each phase is realized through
performing a set of sub-tasks. The human operator detects the
states of the process variables such as FLOW, TEMPERATURE etc. from
the observed (measured) data and fuzzifies them into such terms as
HIGH, LOW, etc. During the fuzzification task the operator, first,
draws mental pictures (i.e. patterns) of the process situations in
his/her mind. Once the approximate pattern of a process situation
is established, the operator, secondly, assesses the clearness of
this pattern, i.e. how clear or vague (fuzzy) the situation is. The
operator generates this clearness assessment based on his/her
understanding and experience of the controlled process and its
operation. This is usually achieved through using heuristic
measures of clearness during the assessment. The more
understandable and clearer the detected situation pattern is the
more confident and clearer pattern of the control action the
operator will generate. The operator then matches this pattern with
the fuzzy pattern of the process situation that is already
established in his/her long-term memory (i.e. his/her experience).
The result of performing this pattern matching task is the
generation of fuzzy patterns of the control actions such as
"INCREASE THE FLOW SLIGHTLY", etc. which the operator applies to
the process. Parallel to that the operator assesses the degree of
enforcement of this action.
The model presented in FIG. (1) shows that the procedure of
deducing the control action utilizes the two parallel mechanisms.
The first is the pattern matching by which the operator deduces the
patterns of the control actions (response to what to do). The
second, which is within the basic claims of this invention, is a
mechanism by which the operator deduces the assessment of the
pattern of the control action (response to how clear the deduced
pattern of the control action is). In essence, the second mechanism
achieves a cognitive approximation leading to define the clearness
and importance of the patterns of the control actions depending on
the clearness assessments of the detected patterns of the process
situations. Hence, the output of the deduction phase will be the
pattern of the control action (by applying the pattern matching
mechanism) as well as the clearness assessment of this pattern (by
applying the parallel assessment mechanism). The operator then
utilizes these two outputs to perform the defuzzification task by
which he/she translates (defuzzifies) the fuzzy patterns of control
actions into precise control commands and executes them properly in
the execution phase.
The basic results obtained from this cognitive model are the
definition of the tasks of fuzzy control, the interpretation of
these tasks through the use of the notion of fuzzy patterns and
their clearness assessments, and the identification of the
approximate reasoning performed by the parallel assessment
mechanism. In FIG. (1), the (C.sub.approx) symbol which appears in
the approximate reasoning block refers to the approximate degree of
"strength" or "weakness" of the situation pattern (clearness) which
is used by the assessment mechanism to produce degrees of strength
of the patterns of control actions. The approximate reasoning
mechanism is formulated in this invention as the Clearness
Transformation Rule of Inference (CTRI) and the fuzzy controller
developed on its basis is called the Clearness Transformation Fuzzy
Logic Controller (CTFLC).
The tasks of the CTFLC are defined based on this cognitive model
and summarized in the following order: Fuzzify the measured values
of the process variable to Generate and Assess the fuzzy patterns
of the process situations.fwdarw.Perform pattern matching to infer
the fuzzy patterns of control actions.fwdarw.Apply the parallel
assessment mechanism to Assess the patterns of control
actions.fwdarw.Defuzzify the deduced patterns of the control
actions.fwdarw.Execute the deterministic control actions.
It is within the basic claims of this invention that the CTFLC is a
system capable of handling the tasks and mechanisms defined by the
cognitive model of fuzzy control outlined in the forgoing
description of the invention. In essence, the CTFLC is a cognitive
expert system device which is capable of simulating the human
behaviour in performing the tasks of this model.
THEORETICAL BASES
Fuzzy controllers are designed to operate as follows: receive
measurement data (which are crisp data) from the controlled
process, fuzzify this data to obtain a picture (pattern) of the
process state, take decisions as to what action is required to be
performed on the process, defuzzify this action to obtain crisp
data command, send this crisp data command to regulate the
controlled process.
The CRI based fuzzy controllers implement these tasks as follows:
fuzzify by mapping a crisp data into a vector. To take decision
(i.e. to perform the inference) the control rules and membership
functions should be amalgamated and mapped into a matrix (before
hand) and the decision is made by performing special operations
called the Max-Min operations between the above vector and this
matrix. As a result of these operations another vector is
generated. To obtain the output of the controller in the form of
crisp data many such vectors are generated and some operations are
performed on these vectors to obtain an average value which will be
the crisp data command going to the controlled process.
This procedure implements the tasks of the fuzzy controller by
working on fuzzy data where fuzzy concepts and categories are
represented by data in the form of vectors and matrices. Hence the
term "fuzzy data processing".
The CTFLC controller presented in this invention performs the above
tasks not by fuzzy data processing but by fuzzy pattern processing.
In this design, the fuzzifier produces fuzzy patterns rather than
data vectors. These fuzzy patterns are represented by names or
symbols. The inference procedure consists of two parallel
operations, fuzzy rule inferencing and clearness assessments. The
defuzzification produces exact output data and does not use
averaging or approximation. The design and operation of the
controller is directly based on cognitive foundations. It is a new
look from the angle of cognitive conception which relates the
various functionalities of the fuzzy controller more towards the
human perception of the real world events. The CTFLC fuzzy
controller system uses a set of new developments such as the fuzzy
pattern as a basic entity which is manipulated during operation,
the use of specific measures to assess the clearness degree of a
fuzzy pattern in terms of the "strength" and "weakness", and the
use of a reasoning mechanism which differentiates between the
detected process patterns during on-line operation and the patterns
residing in the controller knowledge-base. These and other
developments which are relevant to the understanding of the
invention are summarized in the next description of the
invention.
The Clearness Degree
The clearness degree characterizes the assessment of the clearness
measure (fuzziness) of a fuzzy pattern. It is a measure of how
close this pattern is to being absolutely clear, partially clear
(fuzzy) or absolutely dim (false). Fuzzy patterns are pictures of
the real world situations with varying degrees of clearness. These
patterns can be assessed using clearness measures built in the
closed interval [0, 1]. A pattern with a clearness degree equal to
1 is the clearest and a pattern with clearness degree equal to zero
is the dimmest. For example, if we define the limits of high
temperature to be between 50.degree.-100.degree. C., then the
temperature 100.degree. C. will have a clearness degree of 1, while
the temperature 50.degree. C. will have the lowest clearness degree
of 0. In other words if we describe the temperature of 50.degree.
C. as high, it will be hardly true according to the above
limits.
To define the clearness degree assume that PA and PB denote fuzzy
patterns which would have the syntax as follows:
PA: Lx is A
PB: Ly is B
and (PA.fwdarw.PB) is a fuzzy implication which is interpreted
syntactically by the fuzzy statement:
IF Lx is A THEN Ly is B
where:
Lx and Ly are linguistic variables defined over the universes of
discourse X and Y, respectively.
A and B are fuzzy subsets of the universes X, Y, respectively. We
note that A and B are linguistic values of Lx and Ly as formulated
by Zadeh (1975).
The clearness degree of the fuzzy pattern is evaluated when the
variable (e.g. Lx) , with which a fuzzy pattern (such as PA) is
associated, is substituted by a measured value, (such as xi). In
this invention we use three measures; C, I and .GAMMA. to estimate
the clearness degree of a fuzzy pattern. C is called the Clearness
Degree, denoted as C(PA), I is called the Integrated Clearness
Degree and denoted as I(PA) and .GAMMA. is the Clearness
Distribution, denoted as .GAMMA.(PA), for a fuzzy pattern PA. FIG.
(5) illustrates the concept of these measures in the assessment of
fuzzy patterns.
The C- measure is used to assess the clearness degree of a fuzzy
pattern and formulated as follows. The fuzzy pattern (PA: Lx is A)
will be associated with a clearness degree, denoted C(PA) when Lx
is substituted by a value x.epsilon.X, which may be represented as
follows:
or:
where: .alpha.k - is a clearness level in the interval [0, 1]. This
interval is divided into a finite set of n clearness-levels
.alpha.i .epsilon. [0, 1] with: ##EQU1## For the I measure: The
clearness degree of a complex pattern (a complex pattern consists
of many elementary patterns, such as the fuzzy controller control
rules) is calculated as follows: ##EQU2## Other formulas such as
probability, statistical etc. can also be employed.
For the .GAMMA.- measure: The fuzzy pattern (PA: Lx is A) may be
represented using the notation of "clearness distribution"
.GAMMA.(PA) as follows. The clearness distribution is generated by
assigning a clearness degree for each measured value x of the
universe of discourse X of the variable Lx. The clearness
distribution .GAMMA.(PA) describes the clearness values of PA for
different values of x.epsilon.X of Lx. Thus for the statement: Lx
is A, if Lx takes the values (x1, x2, . . . , xn) .epsilon.X, and
the clearness degrees for these values are given by:
then the set .alpha.l .epsilon. [0, 1] is the clearness
distribution .GAMMA.(PA) of the fuzzy pattern PA.
Generally the .GAMMA. measure is used to assess the total clearness
distribution of a fuzzy pattern for all the possible values of the
linguistic (process) variable within the range of the fuzzy
pattern, and is given by:
These two measures are used by the CTFLC to assess the clearness of
any complex fuzzy pattern described formally as a well formulated
formula (wff) of the logic of fuzzy predicates.
The Approximate Reasoning Mechanism
While the CRI performs inferencing (approximate reasoning) by using
vectors and matrices, the approximate reasoning presented in this
invention, the Clearness Transformation Rule of Inference (CTRI),
comprises of two parallel mechanisms. These are the "Pattern
Matching" and the "Clearness Transformation" mechanisms. The output
of the pattern matching mechanism is the control action pattern and
the output of the transformation mechanism is the clearness degree
of the control action pattern. The transformation mechanism assigns
the clearness degree of the detected pattern of the process
situation (observation) to the pattern of the control action. This
mechanism follows the approximate reasoning process that the human
operator performs in the pattern matching activity which is
reflected in the cognitive model of fuzzy control mentioned in the
foregoing description of the invention and illustrated in FIG.
(1).
To state the CTRI formally, the general form of a Situation-Action
rule of the fuzzy controller is as follows:
or
where:
PAi - are fuzzy patterns of the general form "Lx.sub.i is A.sub.i "
used to describe the patterns of the process variables (process
situation), and i=1, 2, . . . , N.
PBj - are fuzzy patterns of the general form "Lyj is Bj" used to
describe the patterns of control actions, j=1, 2, . . . , M.
Now, given two fuzzy patterns P1 and P2, where:
P1: is a pattern of the fuzzy controller rule of expression (0,
i.e.
P1=<Situation Pattern.fwdarw.Control Action Pattern>.
P2: is a pattern of a process situation given with its clearness
distribution (.GAMMA.), i.e.
P2=<Situation Pattern> and .GAMMA.(P2).
If these two patterns are applied to the CTRI, the CTRI will
deduce:
P3: a pattern of the control action with an assessment of its
clearness distribution equal to that of P2, i.e.
P3=<Pattern of the Control Action> with
.GAMMA.(P3)=.GAMMA.(P2).
Using the symbolic notations of the Logic of Fuzzy Predicates, the
CTRI mechanism is stated as follows:
Given two fuzzy patterns (Well Formulated formula of the logic of
fuzzy predicates): ##EQU3## where: G, H and G.fwdarw.H are patterns
of the fuzzy controller rules specified by the clearness
distributions .GAMMA.(G) and .GAMMA.(H); G' and H' are measurement
patterns of G and H, respectively.
Since the clearness distribution is the collection of clearness
degrees, expression (2) is also applicable when we replace .GAMMA.
by C.
The application of the CTRI for approximate reasoning in the CTFLC
offers many advantages to this device. First it gives it the
cognitive inference property in deducing the clearness degrees of
the inferred patterns of the control actions. This enables it to
produce the patterns of decisions together with their clearness
degrees (validity). The clearness degree of the fuzzy pattern
during on-line operation may exceed the clearness degree of the
pattern residing in the knowledge-base of the controller (the
experience). This feature gives the CTFLC higher intelligence than
other designs of fuzzy controllers which do not possess this
capability. Secondly, the CTRI performs reasoning at the level of
fuzzy pattern processing. This feature makes it possible to compare
the behaviour of the CTFLC with the human expert involved in
decision-making procedures in the same domain. Having such
advantages makes these devices more compatible with the human
behaviour and act as a support to this behaviour.
DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT OF THE CTFLC
The architecture and operational phases of the CTFLC system for
handling the tasks of the cognitive model of fuzzy control are
illustrated in FIG. (2). This system consists of the following
modules: The Fuzzifier, The Controller Pattern Matching Mechanism,
The Parallel Assessment Mechanism for Approximate Reasoning and the
Defuzzifier. The controller operates in a cycle which consists of
four phases: Fuzzification, Rule Selection and Inference, Parallel
Approximate Reasoning and Defuzzification. The flow of data and
control between these four modules is coordinated by a Control and
Inference module. The internal organization of the fuzzy controller
is presented in FIG. (3). The knowledge-base is organized so that
each module of the controller is attached to the portion of
knowledge it requires to access in order to perform its task. This
organization reflects the design of a truly artificial intelligence
system whereby each of its modules has its own distinct
knowledge-base, making the whole system transparent to changes in
the various knowledge bases and to the effects of these changes.
This has a paramount importance in the simplification of generating
and optimizing (tuning) the various knowledge bases for each
task.
An overall account of the operation of the controller is
illustrated in FIG. (2) and summarized as follows. The controller
receives crisp data which represents the measured, or calculated,
values of the controlled process variables. This data is channeled
to the Fuzzifier module which performs two operations on it. First
it generates the description of the fuzzy pattern of each process
variable. Second it assesses the clearness degrees of the generated
patterns (estimated over the interval [0, 1]). The first output of
the Fuzzifier (the situation fuzzy patterns) are channeled to the
Pattern Matching module to deduce the fuzzy pattern of the control
action using forward chaining. The second output of the fuzzifier,
which is the clearness degrees of the situation patterns, is
channeled to the assessment mechanism module. This module selects
the minimum of the clearness degrees it receives. This minimum
clearness degree is assigned to the pattern of control action.
Finally, the Defuzzifier module receives the patterns of the
inferred control action (generated by the Pattern Matching
Mechanism) and their clearness degree (generated by the assessment
Mechanism) and deduces the crisp data (command) of the control
actions. This command is then sent to regulate the process.
Each of the above tasks of the CTFLC is analyzed in terms of the
Input/Output relation, portion of knowledge needed and the
appropriate reasoning model used to achieve it. The results are
summarized in Tables 1, 2 and 3 of FIG. (4). These tables cover the
data, knowledge and control strategies required by the CTFLC system
to perform each task.
Unlike the fuzzifier of the CRI based fuzzy controller which
generates vectors for the controller to operate on to produce its
output using multi-dimensional matrices, the fuzzifier of the CTFLC
controller generates fuzzy patterns which are acted on by the
controller directly to produce its output. The controller here
processes the fuzzy patterns rather than fuzzy data, which makes it
more in line with truly simulating human decision making.
Next we describe the design and operating phases of the CTFLC in
some details. During the Fuzzification Phase, the process
measurement crisp data (x.sub.1, x.sub.2, . . . , x.sub.N) are
fuzzified to generate the fuzzy patterns (PA'.sub.1, PA'.sub.2, . .
. , PA'.sub.N) of the process situation (observation). The
generated situation pattern is matched with the controller pattern
(PA.sub.1, PA.sub.2, . . . , PA.sub.N) which is the LHS of the
controller rules. This fuzzification is achieved through the
generation of the clearness degree assessment C(PA'.sub.i) of the
measured value x.sub.i for each fuzzy pattern PA'.sub.i using their
clearness degrees as follows. Since, in general, there is a finite
set of fuzzy patterns (and their clearness degrees) associated with
each linguistic (process) variable Lx.sub.i, the Fuzzifier selects
the fuzzy pattern PA'.sub.i which has the maximum clearness degree
value (e.g. .alpha..sub.i max) for the crisp data of the process
measurement xi. The fuzzy patterns (PA'.sub.1, PA'.sub.2, . . . ,
PA'.sub.N) which are generated in this way for N variables
constitute the detected fuzzy pattern of the process situation
(this is a complex pattern made of many elementary patterns). The
Fuzzifier also generates {C(PA'.sub.i)max} which is the set of
clearness degree measures <.alpha..sub.1 max, .alpha..sub.2 max,
. . . , .alpha..sub.n max>, where: .alpha..sub.n max
.epsilon.[0, 1]. This set constitutes the clearness degree of the
fuzzy pattern of the process situation.
In more details, FIG. (5) shows the block diagram of the Fuzzifier
Module. The input to the Fuzzifier is the crisp data (x.sub.1, . .
. , x.sub.N) where each x.sub.i represents the current measurement
value of an input variable Lx.sub.i, i=1, . . . , N. The output is
two components. The first is a set of fuzzy patterns of the process
situation such as (PA'.sub.1, . . . , PA'.sub.n). The second is a
set of clearness degrees (C(PA'.sub.1)max, . . . , C(PA'.sub.n)max)
which are the maximum clearness degrees of the fuzzy patterns.
These two outputs are produced by two rule-based modules:
Fuzzifier-I and Fuzzifier-II, respectively. They operate in two
cycles so that Fuzzifier-I (cycle 1) generates the fuzzy pattern
(PA'.sub.i). This fuzzy pattern together with the measured value of
the process variable serve as inputs to Fuzzifier-II to begin cycle
2 in which the clearness degree value C(PA'.sub.i)max is generated.
For N variables these two cycles are repeated N times.
To achieve the tasks of fuzzifier-I we compute the intersection
points between every two adjacent clearness degree curves of the
fuzzy patterns that are associated with each linguistic (process)
variable. We refer to these intersections points as the thresholds
of Transition (TT). In essence, these IT points indicate the
existence of a transition between the fuzzy patterns (PA.sub.h),
(h=1, 2, . . . H), which describe the state of each process
variable Lx.sub.i (i=1, 2, . . . , N). FIG. (6) shows the
derivation of the TT values for the variable Lx.sub.i which has
three (H=3) fuzzy patterns: PLOW, PNORMAL and PHIGH. In this figure
two of these thresholds are projected on the domain space X
(x-axis) and denoted as:
TT.sub.L,N =The Threshold of Transition between .GAMMA.(PLOW) and
.GAMMA.(PNORMAL)
TT.sub.N,H =The Threshold of Transition between .GAMMA.(PNORMAL)
and .GAMMA.(PHIGH).
The Fuzzifier recognizes the fuzzy pattern PA.sub.h which describes
the current state of the variable Lx.sub.i by deciding the interval
(between two TT points) to which the value xi, which is acquired
from the process, belongs. This approach facilitates the
implementation of a one-to-one mapping so that for each measured
value x.sub.i there is only one pattern PA.sub.i which describes
the current state of the variable Lx.sub.i. This procedure can be
implemented simply by comparing the value of xi with the values of
the thresholds (TT). The following generic rule is employed to
implement this procedure:
where: TTh-1, h and TT h,h+1 refer to the values of the thresholds
of transition (TT) between the fuzzy patterns PA.sub.h-1, PA.sub.h
and PA.sub.h, PA.sub.h+1, respectively. For the example illustrated
in FIG. (6), three such rules are derived. They are:
______________________________________ R1: IF 0 .ltoreq. xi <
TT.sub.L,N THEN P.sub.LOW R2: IF TT.sub.L,N .ltoreq. xi <
TT.sub.N,H THEN P.sub.NORMAL R3: IF TT.sub.N,H .ltoreq. xi THEN
P.sub.HIGH ______________________________________
Similar rules can be derived for all process variables.
The on-line operation of Fuzzifier-I to generate the fuzzy patterns
is accomplished by matching the crisp data xi coming from the
process with these rules. The result of this matching is the set of
fuzzy patterns (PA'.sub.1, PA'.sub.2, . . . , PA'.sub.N) which
constitute the description of the situation pattern. We note that
these rules also generate fuzzy patterns PA'.sub.i which have
maximum clearness degrees C(PA'.sub.i) max for a given process
measurement x.sub.i, i=1, 2, . . . , N, (these patterns are
generated as best describing the state of process variables).
Next we describe the design of Fuzzifier-II which generates the
clearness degrees of the fuzzy patterns. These are the set of the
clearness degrees (C(PA'.sub.1)max, C(PA'.sub.2)max, . . . ,
C(PA'.sub.N)max), which are assessed over the interval [0, 1]. For
Fuzzifier-II to operate, the interval [0, 1] is descretized and
projected on the domain space X.sub.i of the clearness distribution
.GAMMA.(PA.sub.i) for each fuzzy pattern. The values obtained are
referred to as the "Clearness level Thresholds" (CL). FIG. (7)
shows an example of the projection of five clearness thresholds
(.alpha..sub.1, . . . , .alpha..sub.5) on the domain of
.GAMMA.(PHIGH). The result is five clearness threshold values
(CL.sub.1, . . . , CL.sub.5) on X.sub.i (CL should not be confused
with the thresholds of transition TT between the clearness degrees
defined earlier). These threshold points are used to generate
C(PA'.sub.i)max by employing simple comparison between the measured
value x.sub.i and these CL values to decide to which interval
(between these points) the data x.sub.i belongs. The detected
intervals indicate values of clearness thresholds in the interval
[0, 1]. The rules employed by Fuzzifier-II to perform this task
have the following generic form:
where: FP stands for "Fuzzy Pattern".
As an example, the following rules are generated for .GAMMA.(PLOW)
of FIG. (7).
R1: IF The FP is PHIGH and x.sub.i <CL.sub.1 THEN
C(PHIGH)=.alpha..sub.0
R2: IF The FP is PHIGH and CL.sub.1 .ltoreq.x.sub.i <CL.sub.2
THEN C(PHIGH)=.alpha..sub.1
R3: IF The FP is PHIGH and CL.sub.2 .ltoreq.x.sub.i <CL.sub.3
THEN C(PHIGH)=.alpha..sub.2
R4: IF The FP is PHIGH and CL.sub.3 .ltoreq.x.sub.i <CL.sub.4
THEN C(PHIGH)=.alpha..sub.3
R5: IF The FP is PHIGH and CL.sub.4 .ltoreq.x.sub.i <CL.sub.5
THEN C(PHIGH)=.alpha..sub.4
R6: IF The FP is PHIGH and CL.sub.5 .ltoreq.x.sub.i THEN
C(PHIGH)=.alpha..sub.5
Evidently, the number of rules of Fuzzifier-II for each fuzzy
pattern depends on the number of clearness thresholds used to
descretize the clearness degree of the pattern. The number of
clearness thresholds can be chosen as large as desired depending on
the required accuracy without the fear of increasing the
computation time considerably.
Next we describe the Rule Selection phase. During this phase the
appropriate rule is selected by matching the generated pattern of
the process situation (PA'.sub.1, PA'.sub.2, . . . , PA'.sub.N)
with the pattern (PA.sub.1, PA.sub.2, . . . , PA.sub.N) of the
controller rules. The RHS of the matching rule is activated which
describe the pattern(s) PB.sub.j of the control action(s). The
Controller rules describe the association between fuzzy patterns of
the process situations and the control actions. The control
protocol of the CTFLC system is composed of a finite set of fuzzy
rules of the form:
Both the pattern of the "Process Situation" and the pattern of the
"Control Action" are defined in the general form of a
Situation-Action rule of the control protocol of equation (1).
Next we describe the Approximate Reasoning Phase in which the
Parallel mechanism scheme is applied. This scheme computes a value
from the clearness degrees <.alpha..sub.1 max, .alpha..sub.2
max, . . . , .alpha..sub.n max> generated by the fuzzifier and
assigns it to the inferred pattern of the control action. The
designer can choose this value to be the minimum, maximum or the
average as described in the forgoing description of the invention
under the section of clearness degree.
However, in this invention the CTRI uses the minimum value given
below:
or,
This clearness degree carries the information leading to the
computation of the exact value of the control command signal.
In the Defuzzification Phase the inputs to the Defuzzifier are the
pattern of the control action PB'.sub.j and its computed clearness
degree C(PB'.sub.j). The output of the defuzzifier is the crisp
data value y' of the control variable Ly.sub.j. The Defuzzifier
infers this value by reflecting the value of C(PB'.sub.j) on the
clearness degree curve (the y-axis) and obtaining the result using
its projection on the domain space (the x-axis).
Next we describe the defuzzifier operation in some details. The
Defuzzifier Module (see FIG. 8) receives the pattern of the control
action PB'.sub.j and its clearness degree value C(PB'.sub.j) as
inputs. The output is the crisp data y' which represents the
control command going to the controlled process. The
defuzzification is achieved by counter reflecting the C(PB'.sub.j)
value on the clearness degree axis .GAMMA.(PB'.sub.j) and
projecting it onto the domain space (x-axis) to infer the crisp
value y' for the control variable Lyj. The clearness degree curve
of the action pattern is descretized into K-clearness levels,
{.alpha.k}, k=1,2, . . . , K. These clearness levels are projected
on the variable domain space (the x-axis) so that each level is
associated with a set of values {yj} of this domain. A particular
variable value y' is inferred when the value of C(PB'.sub.j) refers
to a certain clearness level. This task is achieved by using the
following generic rule:
where, the value of y'j is generated from the boundaries [yk,
yk+1].
Hence, the rules employed by the Defuzzifier module establish an
association between the value of C(PB.sub.j) and the relevant value
y' of the control variable. FIG. (9) illustrates how six such rules
are derived when C(PB.sub.j) is descretized into six levels. The
six rules for this example are:
IF The pattern is PB'.sub.j and 0.ltoreq.C(PB'.sub.j)<.alpha.1
THEN y'.ltoreq.y1
IF The pattern is PB'.sub.j and
.alpha.1.ltoreq.C(PB'.sub.j)<.alpha.2 THEN
y1.ltoreq.y'.ltoreq.y2
IF The pattern is PB'.sub.j and
.alpha.2.ltoreq.C(PB'.sub.j)<.alpha.3 THEN
y2.ltoreq.y'.ltoreq.y3
IF The pattern is PB'.sub.j and
.alpha.3.ltoreq.C(PB'.sub.j)<.alpha.4 THEN
y3.ltoreq.y'.ltoreq.y4
IF The pattern is PB'.sub.j and
.alpha.4.ltoreq.C(PB'.sub.j)<.alpha.5 THEN
y4.ltoreq.y'.ltoreq.y5
IF The pattern is PB'.sub.j and .alpha.5.ltoreq.C(PB'.sub.j) THEN
y5.ltoreq.y'
The number of discrete levels is accuracy dependent, i.e. for more
accurate control commands the number of discrete levels is
increased to any required limit.
The CTFLC is designed to have a special database module which
provides a complete record of the behaviour of the controller at
each phase of operation (FIG. 10). At the beginning of each control
cycle, the database contains only the current values of process
variables. By the completion of the fuzzification phase, for
example, it will contain a list of the fuzzy patterns which
describe the process situation and the clearness degrees of these
patterns. At the completion of the control cycle, the information
in this database serves as an excellent record for the
implementation of a backtracking chronological explanation of the
controller operation and decision.
The controller operation and control described so far are
coordinated by a Control and Inference Module (see FIG. 2). This
module is the control core of the system. It coordinates the
operations of the modules and the succession of the four phases of
the controller. It applies the appropriate reasoning strategy to
execute each phase of the controller in the appropriate sequence so
that the full controller cycle is realized. It also arranges access
to the knowledge required to perform each task. The module also
updates the controller database with the data obtained through the
execution of each phase.
* * * * *